Seven years late!) but none of these answers gives a comprehensive explanation, particularly in that the OP's premise "westbound travel is slower" is only correct at certain latitudes.
This diagram shows the macro air circulation patterns around the globe. Generally, air is heated at the equator and rises, then travels at high altitude towards the poles. At about 30deg latitude the air mass has cooled sufficiently that it wants to descend, then heads at low altitudes back towards the equator. This is the Hadley cell. From space, these airflows appear largely Northly and Southerly. On Earth, the Coriolis effect makes the airflow also appear Easterly and the result is called the Trade Winds. Here, westbound air travel is faster than eastbound.
Similarly, air is cooled at the poles and descends, then travels at low altitude toward the equator to approximately 60deg latitude where warming makes the air rise. This is the Polar cell. The same low altitude direction toward the equator and the same Coriolis effect makes these wind directions match the Trades, and they are called the Easterlies.
Polar and Hadley are driven by polar cold and equatorial heat. If the Earth were smaller they would combine into one cell. At the existing scale an intermediate cell forms, the Ferrel cell, and its direction is driven by contact with Polar and Hadley at 30deg and 60deg.
Polar makes a "chimney" at 60deg which is shown on the chart as low pressure. Hadley makes a downdraft at 30deg, shown as high pressure. The Ferrel air mass flows from high pressure to low, or toward the poles at low altitude. With airflow reversed the Coriolis effect now makes the winds appear westerly, and are aptly called the Westerlies. This is where air travel in the US and Europe occurs, and this is where the OP's "westbound travel is slower" applies.
So both atmospheric heating/cooling and the Earth's rotation via the Coriolis effect determine the direction of the prevailing winds, and consequently the amount of time air travel takes in a particular direction.